Improved Sobolev regularity for linear nonlocal equations with VMO coefficients

Nowak SN (2022)
Mathematische Annalen .

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Abstract / Bemerkung
This work is concerned with both higher integrability and differentiability for linear nonlocal equations with possibly very irregular coefficients of VMO-type or even coefficients that are merely small in BMO. In particular, such coefficients might be discontinuous. While for corresponding local elliptic equations with VMO coefficients such a gain of Sobolev regularity along the differentiability scale is unattainable, it was already observed in previous works that gaining differentiability in our nonlocal setting is possible under less restrictive assumptions than in the local setting. In this paper, we follow this direction and show that under assumptions on the right-hand side that allow for an arbitrarily small gain of integrability, weak solutions u is an element of W-s,W-2 in fact belong to W-loc(t, p) for any s <= t < min{2s, 1}, where p > 2 reflects the amount of integrability gained. In other words, our gain of differentiability does not depend on the amount of integrability we are able to gain. This extends numerous results in previous works, where either continuity of the coefficient was required or only an in general smaller gain of differentiability was proved.
Erscheinungsjahr
2022
Zeitschriftentitel
Mathematische Annalen
ISSN
0025-5831
eISSN
1432-1807
Page URI
https://pub.uni-bielefeld.de/record/2961625

Zitieren

Nowak SN. Improved Sobolev regularity for linear nonlocal equations with VMO coefficients. Mathematische Annalen . 2022.
Nowak, S. N. (2022). Improved Sobolev regularity for linear nonlocal equations with VMO coefficients. Mathematische Annalen . https://doi.org/10.1007/s00208-022-02369-w
Nowak, S. N. (2022). Improved Sobolev regularity for linear nonlocal equations with VMO coefficients. Mathematische Annalen .
Nowak, S.N., 2022. Improved Sobolev regularity for linear nonlocal equations with VMO coefficients. Mathematische Annalen .
S.N. Nowak, “Improved Sobolev regularity for linear nonlocal equations with VMO coefficients”, Mathematische Annalen , 2022.
Nowak, S.N.: Improved Sobolev regularity for linear nonlocal equations with VMO coefficients. Mathematische Annalen . (2022).
Nowak, Simon Noah. “Improved Sobolev regularity for linear nonlocal equations with VMO coefficients”. Mathematische Annalen (2022).

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